Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in PYTHON3):

Solution:
import cmath
lineIn = input().split(' ')
numBun = int(lineIn[0])
heightCar = int(lineIn[1])
triA = heightCar/2
AreaPer = triA/numBun
proportion = 1/heightCar
prevHeights = 0
answer = []
def calcHeightTrapez(area, prevHeights):
    a = prevHeights*proportion
    #area = (prevHeights*proportion+(height + prevHeights)*proportion)/2 * height
    #area = (prevHeights*proportion)*height + (height*proportion)/2 * height
    #0 = (proportion/2)*height**2 + a*height - area
    d = (a**2) - (4*(-area)*(proportion/2))
    sol1 = (-a + d**(1/2))/(proportion)
    #sol2 = -a - cmath.sqrt(d)/(proportion)
    return sol1
    
def calcIso(area):
    height = (area * 2 / proportion)**(1/2)
    return height
prevHeights = calcIso(AreaPer)
answer.append(prevHeights)
for i in range(1, numBun-1):
    prevHeights += calcHeightTrapez(AreaPer, prevHeights)
    answer.append(prevHeights)
print(" ".join(map(str, answer)))